Formation control via distributed optimization of alignment error

This paper proposes a method for the stabilization of vehicle formations in the plane under a fixed, but not necessarily complete, sensing graph. In this method each agent acts to minimize a local alignment error function that measures the difference between the desired relative formation of the agent and its neighbors (as determined by a sensing graph) and their current positions. It is shown that if the agents are modeled as discrete time single integrators then each agent attempting to reduce its local alignment error results in a consensus algorithm that monotonically drives the total alignment error to zero.